Trichloroacetic acid $\left(\mathrm{CCl}_3 \mathrm{CO}_2 \mathrm{H}\right)$ is a corrosive acid that is used to precipitate proteins. The pH of a $0.050-M$ solution of trichloroacetic acid is the same as the pH of a $0.040-\mathrm{M} \mathrm{HClO}_4$ solution. Calculate $K_{\mathrm{a}}$ for trichloroacetic acid.